Nonclassical interfacial response in ionic liquids at blocking electrodes

The linear response of a symmetric binary ionic liquid confined between two parallel, blocking electrodes is analyzed under the influence of electrostatic correlations L_{c} while systematically comparing the effects of two distinct interfacial boundary conditions: the Bazant-Storey-Kornyshev (BSK) boundary condition, corresponding to the vanishing correlation limit, and the de Souza-Bazant (dSB) boundary condition, which incorporates finite electrostatic correlation effects at charged electrode surfaces. In contrast to conventional weakly nonlinear models involving thin-double-layer scalings based on small parameters λ_{D}/L≪1 or sqrt[λ_{D}L_{c}]/L≪1, where λ_{D} denotes the Debye screening length and L is the half-cell thickness, the present formulation accommodates double layers of arbitrary width. Using matched asymptotic expansions at leading order, both the frequency-dependent response and the equilibrium response are derived in the asymptotic limit ɛ=L_{c}/L≪1. This separation of length scales gives rise to interfacial dynamics and equilibrium characteristics that are not captured by standard Debye-based asymptotic models. In particular, the frequency response exhibits a low-frequency inductive behavior manifested by a negative real impedance, a negative complex capacitance, and a nonmonotonic phase response, with these effects being significantly enhanced under the dSB boundary condition. The origin of the inductive regime is linked to the emergence of a low-frequency chemical-inductor contribution, which introduces an intrinsic slow dynamical process. Together with the fast Debye timescale serving as the reference scale, this leads to a coupled fast-slow dynamical structure that becomes increasingly pronounced with growing electrostatic correlation length L_{c}. A scaling analysis in the low-frequency regime further identifies a distinguished intermediate relaxation timescale L_{c}^{2}/D in the strong-correlation regime, where D denotes the diffusion coefficient of the ion species. At equilibrium, the dSB boundary condition likewise predicts a nonclassical negative differential capacitance that is absent under the BSK boundary condition.